O-Level Additional Math

[Kafer]

John spwes ia x m/s.

Mary speed ia y m/s
If john starts 2 sec later, he will take 8 secs to catch up with mary.
If john starts to run only when mary is 8m ahea 5 sec to catch up with her.
Form two eqn in x an y.

[greenflora]

Hi, can anyone help with this question?


The scale of map X is 1 : x and the scale of map Y is 4 : y.
If the actual area of a park is represented by 10cm^2 and 2.5cm^2 on maps X and Y respectively, find x : y in its simplest form.

[JadeDry]

Hello,


I would appreciate help with the following question:

Find the values of x and y-

((2/3)x) - ((3/5)y) - 4 = ((1/20)x) - y + (17/30) = 2x - y - (18 + (14/15))

I would greatly appreciate a step-by-step answer.

Thanks in advance.

[JadeDry]

Hello again, I have one more question with which I would appreciate some assistance.


Find the values of x and y-

((2/7)x) + ((3/4)y) - 4 = ((3/5)x) - ((2/7)y) - 44 = ((7/15)x) + y - (3 + (1/3))

I would greatly appreciate a step-by-step answer as before.

Thanks in advance.

[red rose]

Would appreciate help for these 2 Qs.


1) The polynomial 3x^2-9x+2 has the same remainder when divided by x-p or by x+4q, where p is not equal to -4q. Find the value of p-4q.
2) When a polynomial f(x) is divided by x+1 and x+2, the remainders are 3 and 5 respectively. Find the remainder when f(x) is divided by x^2+3x+2.

Thanks!

[awesomeguy]

Sec 2 Express Math Qn Proportion


For an adventure camp, food is bought to last for 15 days for a group of 40 students. \tIf 4 students left the camp after 6 days, how many days can the food last for the \tremaining 36 students?

Please help. Thanks

[awesomeguy]

Sec 2 Express Math Qn Proportion


For an adventure camp, food is bought to last for 15 days for a group of 40 students. \tIf 4 students left the camp after 6 days, how many days can the food last for the \tremaining 36 students?

Please help. Thanks

[jieheng]

awesomeguy:

Sec 2 Express Math Qn Proportion


For an adventure camp, food is bought to last for 15 days for a group of 40 students. \tIf 4 students left the camp after 6 days, how many days can the food last for the \tremaining 36 students?

Please help. Thanks

Total amount of food = 40*15 = 600

The amount of food already consumed by 40 students on the first 6 days
= 40*6
=240

No of days that the food can last for the remaining 36 students
=(600-240)/ 36
=360 / 36
=10 (Ans)

[jieheng]

red rose:

Would appreciate help for these 2 Qs.


1) The polynomial 3x^2-9x+2 has the same remainder when divided by x-p or by x+4q, where p is not equal to -4q. Find the value of p-4q.
2) When a polynomial f(x) is divided by x+1 and x+2, the remainders are 3 and 5 respectively. Find the remainder when f(x) is divided by x^2+3x+2.

Thanks!

1)

f(x) = 3x^2 -9x +2

f(p) = f(-4q)
3p^2 -9p +2 = 3(-4q)^2 -9(-4q) +2
3p^2 -9p - 48q^2 -36q =0
p^2 -3p - 16q^2 - 12q = 0
p^2 - (4q)^2 - 3(p+4q) = 0
(p+4q)(p-4q) - 3(p+4q) = 0
(p+4q)[(p-4q)-3] = 0
p-4q-3 = 0 as p is not equal to (-4q)
p-4q = 3 (Ans)

2)

Let (Ax+B) be the remainder when f(x) is divided by (x^2+3x+2)

f(x) = (x^2+3x+2) Q(x) + (Ax+B)
= (x+1)(x+2) Q(x) + (Ax+B)

f(-1) = A(-1) + B = 3

f(-2) = A(-2) + B = 5

Solving the two equations ,

A = -2 and B = 1

the remainder = -2x + 1 (Ans)

[A concerned mom]

Can anyone help to solve the following Sec 2 questions?


1) Factorise the following expression:

a) 4(x + y)^2 – (1 - x)^2

b) 4x^4 – 12x^2 + 9

c) 12x^2 y^3 – 27x^4 y z^2


2) Factorise each of the following:

a) x^2 – 4 + 2x^3 + 4x^2

b) 6cd – 16d - 8c + 12d^2

c) 4c^2 d^2 - 49d^2 - 14cd - 49d

d)16c^2 – 16cd + 4d^2 – 49c^4

Note: ^ denotes "to the power of"

Appreciate your help